To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints using these variables.

Let's define:
- $x_1$ as the number of packages X sold.
- $x_2$ as the number of packages Y sold.

The objective is to maximize profit. The profit from selling one package X is $70, and from selling one package Y is $120. Therefore, the total profit can be represented by the objective function:
\[ \text{Maximize: } 70x_1 + 120x_2 \]

As for the constraints:
- Each package X contains 5 bottles of green tea, and each package Y contains 3 bottles of green tea. The shop only has 1200 bottles of green tea available.
- Each package X contains 2 bottles of black tea, and each package Y contains 4 bottles of black tea. The shop only has 900 bottles of black tea available.

Thus, the constraints can be represented as:
1. Green tea constraint: $5x_1 + 3x_2 \leq 1200$
2. Black tea constraint: $2x_1 + 4x_2 \leq 900$

Additionally, we have non-negativity constraints since the number of packages sold cannot be negative:
- $x_1 \geq 0$
- $x_2 \geq 0$

Now, let's represent this in the requested JSON format:

```json
{
    'sym_variables': [('x1', 'number of packages X'), ('x2', 'number of packages Y')],
    'objective_function': '70*x1 + 120*x2',
    'constraints': ['5*x1 + 3*x2 <= 1200', '2*x1 + 4*x2 <= 900', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Tea_Shop_Optimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Packages_X")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Packages_Y")

# Set the objective function
m.setObjective(70*x1 + 120*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 3*x2 <= 1200, "Green_Tea_Constraint")
m.addConstr(2*x1 + 4*x2 <= 900, "Black_Tea_Constraint")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of Packages X: {x1.x}")
    print(f"Number of Packages Y: {x2.x}")
    print(f"Maximum Profit: ${70*x1.x + 120*x2.x:.2f}")
else:
    print("No optimal solution found")
```